Problem: On the way to school, Karen became fixated on the puzzle game on her phone!

<image>

The game is played as follows. In each level, you have a grid with n rows and m columns. Each cell originally contains the number 0.

One move consists of choosing one row or column, and adding 1 to all of the cells in that row or column.

To win the level, after all the moves, the number in the cell at the i-th row and j-th column should be equal to gi, j.

Karen is stuck on one level, and wants to know a way to beat this level using the minimum number of moves. Please, help her with this task!

Input

The first line of input contains two integers, n and m (1 ≤ n, m ≤ 100), the number of rows and the number of columns in the grid, respectively.

The next n lines each contain m integers. In particular, the j-th integer in the i-th of these rows contains gi, j (0 ≤ gi, j ≤ 500).

Output

If there is an error and it is actually not possible to beat the level, output a single integer -1.

Otherwise, on the first line, output a single integer k, the minimum number of moves necessary to beat the level.

The next k lines should each contain one of the following, describing the moves in the order they must be done:

  * row x, (1 ≤ x ≤ n) describing a move of the form "choose the x-th row". 
  * col x, (1 ≤ x ≤ m) describing a move of the form "choose the x-th column". 



If there are multiple optimal solutions, output any one of them.

Examples

Input

3 5
2 2 2 3 2
0 0 0 1 0
1 1 1 2 1


Output

4
row 1
row 1
col 4
row 3


Input

3 3
0 0 0
0 1 0
0 0 0


Output

-1


Input

3 3
1 1 1
1 1 1
1 1 1


Output

3
row 1
row 2
row 3

Note

In the first test case, Karen has a grid with 3 rows and 5 columns. She can perform the following 4 moves to beat the level:

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In the second test case, Karen has a grid with 3 rows and 3 columns. It is clear that it is impossible to beat the level; performing any move will create three 1s on the grid, but it is required to only have one 1 in the center.

In the third test case, Karen has a grid with 3 rows and 3 columns. She can perform the following 3 moves to beat the level:

<image>

Note that this is not the only solution; another solution, among others, is col 1, col 2, col 3.

Solution (in JAVA):

Solution:
import java.util.Scanner;

public class puzzle {

    static int count = 0;
    
    public static void main(String[] args) {
        // TODO Auto-generated method stub
        Scanner scan = new Scanner(System.in);
        int rows = scan.nextInt();
        int cols = scan.nextInt();
        int[][] grid = new int[rows][cols];
        for (int i = 0; i < rows; i++) {
            for (int j = 0; j < cols; j++) {
                grid[i][j] = scan.nextInt();
            }
        }
        StringBuilder builder = new StringBuilder();
        
        if (rows < cols) {
            parseRows(grid, builder);
            parseCols(grid, builder);
        }
        else {
            parseCols(grid, builder);
            parseRows(grid, builder);
        }
        
        
        if (!isValidGrid(grid)) {
            System.out.println(-1);
        }
        else {
            System.out.println(count);
            System.out.println(builder.toString());
        }
        
        
        //Make sure to count from 1 when outputting answer
    }
    
    public static void printRow(int index, StringBuilder b) {
        b.append("row " + (++index) + '\n');
        count++;
    }
    
    public static void printCol(int index, StringBuilder b) {
        b.append("col " + (++index) + '\n');
        count++;
    }
    
    public static int minOnRow(int[][] grid, int rowIndex) {
        int min = grid[rowIndex][0];
        for (int j = 1; j < grid[0].length; j++) {
            if (grid[rowIndex][j] < min) {
                min = grid[rowIndex][j];
            }
        }
        return min;
    }
    
    public static int minOnCol(int[][] grid, int colIndex) {
        int min = grid[0][colIndex];
        for (int i = 1; i < grid.length; i++) {
            if (grid[i][colIndex] < min) {
                min = grid[i][colIndex];
            }
        }
        return min;
    }
    
    public static boolean isValidGrid(int[][] grid) {
        for (int i = 0; i < grid.length; i++) {
            for (int j = 0; j < grid[0].length; j++) {
                if (grid[i][j] != 0) {
                    return false;
                }
            }
        }
        return true;
    }
    
    public static void parseRows(int[][] grid, StringBuilder builder) {
        for (int i = 0; i < grid.length; i++) {
            int minOnRow = minOnRow(grid, i);
            for (int t = 0; t < minOnRow; t++) {
                printRow(i, builder);
            }
            for (int j = 0; j < grid[0].length; j++) {
                grid[i][j] -= minOnRow;
            }
        }
    }
    
    public static void parseCols(int[][] grid, StringBuilder builder) {
        for (int j = 0; j < grid[0].length; j++) {
            int minOnCol = minOnCol(grid, j);
            for (int t = 0; t < minOnCol; t++) {
                printCol(j, builder);
            }
            for (int i = 0; i < grid.length; i++) {
                grid[i][j] -= minOnCol;
            }
        }
    }
    
    
    
    

}